Semi Blind Channel Estimation: An Efficient Channel Estimation scheme for MIMO- OFDM System

Transcription

1 Australian Journal of Basic and Alied Sciences, 7(7): , 03 ISSN Semi Blind Channel Estimation: An Efficient Channel Estimation scheme for MIMO- OFDM System Arathi. Devasia, Dr.G. Ramachandra Reddy School of Electronics Engineering, VI University, Vellore-6304, amilnadu, India. Abstract: In this aer, an efficient channel estimation scheme for MIMO OFDM system has been resented. he semi-blind channel estimation is combination of blind estimation and least square training based channel estimation. Method uses linear rediction for estimating blind constraint and least square (LS) method to estimate A matrix, which is further used to find semi-blind estimate. LS method and semi-blind method are comared based on BER and also mean square error. Results show that when same number of training data is used, semi-blind channel estimation rovide lesser MSE and BER comared to LS method. Key words: Communication channels, orthogonal frequency division multilexing, time varying channel, channel estimation, linear rediction, semiblind. INRODUCION Multi Inut Multi Outut Orthogonal Frequency Division Multilexing (MIMO OFDM) is a strongest cometitor for next generation high seed wireless multimedia communication. It rovides high data rate and high sectral efficiencies. It simlifies the imlementation and is robust against frequency selective channels. Fourth generation wideband communication system uses OFDM along with sace time rocessing. he MIMO OFDM system using multile antennas at the receiver and the transmitter has a romising ability to combat multiath fading and imrove system caacity, bandwidth and ower efficiency. It is well known fact that the transmitted signal gets distorted due to the wireless channel. ence an accurate estimation of wireless channel is essential for MIMO OFDM system erformance. We have three tyes of channel estimation methods namely training based, blind algorithm and the last one, the combination of both revious methods i.e. semiblind channel estimation. raining based algorithm includes least squares (LS), maximum likelihood (ML), minimum mean square error (MMSE) etc. raining based algorithm uses known data i.e. ilots for estimation. At receiver side, the channel is estimated based on how much the known data or the ilots are distorted (I. Barhumi et al., 003) ( Xiaoli Ma et al., 005). raining based channel estimation rovides high accuracy at the cost of bandwidth. More the number of ilots in an OFDM symbol better is the accuracy. On the other hand, blind channel estimation relies on second order statistics, correlation and other roerties. A variety of second order statics (SOS) based blind estimators have been roosed (Karim Abed-Meraim et al., 997) (C. Shin et al., 007) (F. Gao et al., 007) (A. Gorokhov et al., 999). Among all those methods, the noise subsace based method is considered to be the most romising method due to its simle structure and good erformance. Blind estimation gives better sectral efficiency in comarison to training based but has less accuracy. In order to have the advantages of both, the third channel estimation scheme, the semiblind channel estimation was roosed. Semiblind channel estimation is a combination of both training based and blind channel estimation. For same number of ilots, semiblind method rovides better estimation comared to training based method. ence with lower number of ilots we can obtain lower BER in semiblind method. ence better sectral efficiency and accuracy. his aer deals with semiblind channel estimation for MIMO OFDM system based on least squares method and blind channel estimation. Blind channel estimation involves the use of linear rediction rincile along with the noise subsace method. he main idea is to reresent the received signal as a finite order autoregressive (AR) series, rovided the transmitted signals are uncorrelated in time. Using the AR reresentation, linear rediction filter can be derived and hence, can be used for second order deconvolution to estimate the channel (A. Medles et al., 00) (Y. Zeng, et al., 006).Some semiblind channel estimation algorithms (A. Gorokhov et al., 999) have been derived using the combination of linear rediction filter along with higher order statistics on the weighted LS method. he main drawbacks connected to these algorithms are, they require more number of signal samles and they are not robust enough. Incororating blind criterion obtained from linear rediction into training based LS cost function, (A. Medles et al., 00) have roosed semiblind algorithm, which gives a closed form exression for channel estimation for MIMO channel. In these aers, it has been shown that semiblind channel method gives much better channel estimation erformance comared to training based LS method. owever, these aers didn t rovide semiblind channel estimation criteria for MIMO OFDM system and also the determination of weighting factor emloyed to trade off the LS Corresonding Author: Arathi. Devasia, School of Electronics Engineering, VI University, Vellore-6304, amilnadu, India. arathidevasia@gmail.com 53

2 Aust. J. Basic & Al. Sci., 7(7): , 03 and the blind method. Semiblind algorithm derived for MIMO system can t be directly imlemented for MIMO OFDM system, since the signal model is different in both cases. In MIMO OFDM, the ilot signal is added to the signal in frequency domain and then converted to time domain unlike the normal MIMO system. Using Vertical Bell lab Layered Sace ime (VBLAS) MIMO scheme, semiblind channel estimation for MIMO OFDM has been roosed in (F. Wan et al., 007). he major drawback of VBLAS is that, the detection comlexities at the receiver increases exonentially with number of transmit antennas. In this aer, we discuss semiblind channel estimation based on two transmit antenna Alamouti Sace ime Block Coding (SBC) scheme. VBLAS systems can achieve high data rate with accetable BER erformance in a good channel state, whereas SBC systems can achieve better BER erformance even for bad state channels but with lower data rates. he SBC scheme has got very low decoding comlexity and it can be easily imlemented to attain high satial diversity. In this aer, we discuss about semiblind channel estimation for MIMO OFDM emloying least squares and blind algorithm. Second section deals with the MIMO OFDM system model and its related formulations. hree channel estimation techniques (i) training data based least squares method (ii) blind algorithm using linear rediction and noise subsace and (iii) the formulation of semiblind algorithm are discussed in the following sections. Last section deals with the simulation results for validation of the method. his aer will be adoting the following notations. seudoinverse, kroneckor roduct, I n is n n identity matrix, -transose, - conjugate transose, -circular convolution, F -Forbenius norm, vec()-stacking the columns in a matrix together into a vector and E{}-exectation. MIMO OFDM System: Consider a MIMO OFDM system having N transmitting and N R receiving antennas. Usually we take N R greater than N. he time varying channel can be modelled by L-ta finite imulse resonse (FIR) filters. We have a total of N R N FIR filter channels or L set of N R N coefficient matrix ( n) where n=0,, L-. (i R,i ) th element h, ( n) reresents channel imulse resonse from i ir i th transmitting antenna to i R th receiving antenna. Let the transmitted signal vector be reresented as x( n)=[ x ( n),, x ( n)] and received signal vector N be y( n) [ y ( n),, y ( )] N R n. Consider one OFDM symbol with K subcarriers. If we add cyclic refix which is not less than channel length L, then after removing cyclic refix at the receiver, we can write the received signal at the i R th receiving antenna as, N y ( n) h ( n) x ( n) v ( n) () ir ir, i i ir i where n=0,,, K- and v ir is the noise. Unlike MIMO system, MIMO OFDM system involves circular convolution. Least Square Channel Estimation: In OFDM system, the training data i.e ilots are added to the signal in frequency domain and then converted to time domain via IFF block. he frequency domain equation can be written as: Y=X+N () where Y is the received signal, X the transmitted signal, is the Fourier transform of channel imulse resonse and N is the noise. We use comb tye ilot arrangement for LS criterion as it gives better accuracy comared to block tye. hough the channel is fast varying, we assume that channel is constant for two OFDM symbol time eriod. his assumtion is crucial for two transmit Alamouti SBC coding. We now consider signal received at one receiver antenna. Let the number of data in one OFDM symbol transmitted from one transmit antenna be denoted as k and number of ilots be. he ilot locations can be denoted by writing k, k,..., k. he frequency domain reresentation of received signal at ilot locations can be given by, Y i X i N i (3) 53

3 Aust. J. Basic & Al. Sci., 7(7): , 03 Where Y i Yi k Yi k. Yi k for i,,.n R. he transmitted matrix is given by X,, N and j diagxj k Xj k Xj k X X X X for j=,,, N. he noise vector is given by N i Ni k Ni k N i k. i is the ilot location values of Fourier transform of imulse resonse at the i-th receiver. Channel imulse resonse vector can be written as, h h h h i i i in where h ij hij 0 hij. hij L. can be written as i CFM h i M is a maing matrix of dimension N K N L to ad zeros to the channel vector. F is a FF block matrix of size N K N K with K K FF matrix as diagonal blocks. C is a maing matrix of dimension N N K, to extract out the ilot osition Fourier transform values. Equation (3) can be rewritten as Y X CFM h N (4) i i i We now define A X CFM, and we have Y A h N h i i i ls A Yi when rank of A is N L, seudo inverse of A is given by: A A A A and we have h A A A Y (5) ls i We can generalise LS criteria as: Y = Ah +N NR NR NR Y,,,, and noise is given by Y Y Y h. h h h N N N N We have the LS criterion as: Y ˆ Ah whereĥ is the estimated LS channel. Blind Channel Estimation: Let the transmitted signal vector be x( n)=[ x ( n),, x ( n)] consisting of uncorrelated signals and let the N received signal vector be reresented by y( n) [ y ( n),, y ( n)]. We have, for i R- th receiver antenna N R 533

4 Aust. J. Basic & Al. Sci., 7(7): , 03 N y ( n) h ( n) x ( n) v ( n) ir ir, i i ir i. v ir (n) is satio temorally uncorrelated noise with variance v hir,i n reresents channel imulse resonse from i th transmitting antenna to i R th receiving antenna. he idea is to reresent the received MIMO signal as a finite order autoregressive (AR) series rovided the transmitted signals are uncorrelated with resect to time. It imlies we can reresent y(n) as a linear combination of its own finite ast and 0xn where (0) is N R N matrix reresenting the first ta channel coefficients. Now we briefly describe MIMO linear rediction and hence semiblind channel estimation. Let denote the order of linear redictor. Let y n n, n, n y y y he autocorrelation matrix is given by, R n E y n y n and cross correlation matrix as: n R E y n y n MIMO linear redictor W is given by,,, W R R n n W W W (6) Where W (n) for n=,, is N R N R matrix reresenting the coefficient at the n-th ta of rediction filter W. he covariance matrix of the rediction error of y(n) from y(n-) can be given as: δ =R(0) -WR (7) y n R(0) is the autocorrelation matrix of y(n) data given by, 0 E n n R y y Now we can reresent rediction filter as: [ IW ] [ (0) ] (8) where (0) () (L-) 0 0 (0) 0 0 (0) (L-) is a block toelitz matrix of dimension (+)N R (L+)N.As in (Xiaoli Ma et al., 005), the covariance matrix from the above exression can be rewritten as: δ (0) (0) (9) y 534

5 Aust. J. Basic & Al. Sci., 7(7): , 03 Denote the null column sace of (0) as U null. U null can be easily estimated from δ y as in (7). Alying singular value decomosition of δ y we get U null. he eigen vector corresonding to the smallest Eigen value will give U null (noise subsace) and we have U 0 null 0 = (0) Let F 0,., L and Qbe L NR LNR W block toelitz matrix with first block I, W,.., W, 0.., 0. Equation (8) can be rewritten as: column as W Q F 0,,., 0 0 () Using the concet of null column sace and from (0), () can be written as ( I U ) W 0 () L+ null Q F and ( I U ) W can be relaced by W, hence L+ null Q W 0 (3) F Now, in order to vectorise F, we have (3) ( IW )vec( ) 0 (4) F F vec E h, where E is a ermutation matrix of dimension (N N R L) (N N R L) given by h h h h NR and h i hi, 0. hi, L hi, 0. hi, L.. hi,nr 0. hi,nr L. Equation (4) now can be relaced as: ( I W ) E h 0 (5) Bh 0 (6) where arameter B, which is equal to ( IW) E, is the blind constraint on the channel vector h. Semiblind Channel Estimation: he minimum error function for semiblind channel estimation, combining both least square estimation and blind estimation can be given as: ( ˆ) ˆ ˆ ˆ A Y ilot Ah B Bh 0 (7) hˆ In order to minimise the error, differentiating the equation with resect to the estimated channel, we get ( ˆ) ˆ ˆ ˆ ilot hˆ A Y Ah B Bh 0 535

6 Aust. J. Basic & Al. Sci., 7(7): , 03 his can be written as ( ˆ ˆ) ˆ A AB B h A Yilot he semiblind channel is given by ˆ ˆ ˆ (8) h ( A AB B) A Yilot where is a constant whose value lies between 0 and. From (8) it is quite clear that the erformance of semiblind algorithm largely deends on value. Simulation Results: For simulation, we consider a MIMO OFDM system with two transmitter and four receiver antennas. he number of subcarriers in OFDM symbol is 5 and the modulation used is the quaternary hase-shift keying (QSK).he length of cyclic refix is set to ten. he channel model selected is Rayleigh channel model. Channel is characterised by a three ta MIMO-FIR filter, in which each ta corresonds to a 4 random matrix. All the elements in the matrix are indeendent identically distributed (i.i.d.) comlex Gaussian variables with zero mean and unit variance. he order of linear redictor is taken as four. he coding scheme used is SBC Alamouti coding. he estimation erformance is measured in terms of the MSE of the estimate of the channel given by N MC MSE= ˆ n N h h MC n n N MC denotes number of Monte Carlo runs in the simulation. h ˆ n denote estimated channel and h n denote original channel value. MSE versus SNR :- We examine the mean square error for channel estimation as a function of SNR. Simulation has 500 Monte Carlo runs for the transmission of one OFDM symbol. Fig. shows MSE Vs. SNR for two methods, least squares and semiblind. It is clear from the grah that semiblind achieve a better gain in comarison to least squares regardless of the level of SNR. Fig. : MSE versus SNR. 536

7 Aust. J. Basic & Al. Sci., 7(7): , 03 BER Versus SNR: In this exeriment, we study about bit error rate erformance of MIMO OFDM system with resect to SNR. he sace time coding used is Alamouti coding. Simulation consists of 500 Monte Carlo runs over one OFDM symbol. Number ilots used for 5 subcarriers is 8 ilots with a ilot sacing of N=64. Fig. shows the BER erformance for various SNR. It can be clearly understood that semiblind algorithm erforms better than LS algorithm by -5Db. Fig. : BER versus SNR. Conclusion: A semi-blind MIMO-OFDM channel estimation based on blind channel estimation and least squares algorithm has been studied. Blind method uses a combination linear rediction and noise subsace method. A roer formulation of received signals, linear rediction and least squares has been done. he two transmit Alamouti SBC scheme used in simulation has got low decoding comlexity and rovides better BER erformance even for bad state channels in comarison with VBLAS. he semiblind algorithm for MIMO OFDM was simulated and results were comared with least squares (LS) method. he MSE versus SNR and BER versus SNR grah clearly deict the sueriority of semiblind algorithm over LS method. REFERENCES aulraj, A.J., D.A. Gore, R.U. Nabar and. Bolcskei, 004. An overview of MIMO communications-a key to gigabit wireless, roceedings of IEEE, 9(): Barhumi, I., G. Leus and M. Moonen, 003. Otimal training design for MIMO OFDM systems in mobile wireless channels, IEEE ransactions on Signal rocessing, 5(6): ugnait J.K. and B. uang, 000. Multiste linear redictors-based blind identification and equalization of multile-inut multile-outut channels, IEEE ransactions on Signal rocessing, 48(): Xiaoli Ma, Liuqing Yang and Georgios B. Giannakis, 005. Otimal training for MIMO frequencyselective fading channels. IEEE ransactions on Wireless Communication, 4(): ommy, W.S. Chow, Bao-Yun Wang and K.. Ng, 003. Linear rediction Based Multiath Channel Identification Algorithm, IEEE ransaction on circuits and systems-i: Fundamental theory and alications, 50(6): Karim Abed-Meraim, Jean-Francois Cardoso, Alexei Y. Gorokhov, hilie Loubaton and Eric Moulines, 997. On Subsace Methods for Blind Identification of Single-Inut Multile-Outut FIR Systems, IEEE ransactions on signal rocessing, 45(): Shin, C., R.W. eath and E.J. owers, 007. Blind channel estimation for MIMO-OFDM systems, IEEE ransactions on Vehicular echnology, 56(): Gao, F. and A. Nallanathan, 007. Blind channel estimation for MIMO OFDM systems via nonredundant linear recoding, IEEE ransactions on Signal rocessing, 55(): Gorokhov, A. and. Loubaton, 999. Blind identification of MIMO-FIR systems: A generalized linear rediction aroach. Signal rocessing, 73(-):

8 Aust. J. Basic & Al. Sci., 7(7): , 03 Medles, A., D..M. Slock and E. De Carvalho, 00. Linear rediction based semi-blind estimation of MIMO FIR channels. In roceedings of IEEE 3rd Worksho Signal rocess. Adv. Wireless Communication, : Medles, A. and D..M. Slock, 00. Semiblind channel estimation for MIMO satial multilexing systems.in in roceedings of IEEE Vehicular echnology Conference, : Alamouti, S.M., 998. A simle transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communication, 45(9): Zeng, Y., W.. Lam and. Ng, 006. Semiblind channel estimation and equalization for MIMO sacetime coded OFDM. IEEE ransactions on Circuits and systems I, Regular aers, 53(): Wan, F., W.. Zhu and M.N.S. Swamy, 007. Linear rediction based semi-blind channel estimation for MIMO-OFDM system. In roceedings of IEEE International Symosium on Circuits and Systems, :